The randomization and screening of combinatorial DNA libraries is a powerful technique for understanding sequence-function relationships and optimizing biosynthetic pathways. Although it can be difficult to predict a priori which sequence combinations encode functional units, it is often possible to omit undesired combinations that inflate library size and screening effort. However, defined library generation is difficult when a complex scan through sequence space is needed. To overcome this challenge, we designed a hybrid valve- and droplet-based microfluidic system that deterministically assembles DNA parts in picoliter droplets, reducing reagent consumption and bias. Using this system, we built a combinatorial library encoding an engineered histidine kinase (HK) based on bacterial CpxA. Our library encodes designed transmembrane (TM) domains that modulate the activity of the cytoplasmic domain of CpxA and variants of the structurally distant "S helix" located near the catalytic domain. We find that the S helix sets a basal activity further modulated by the TM domain. Surprisingly, we also find that a given TM motif can elicit opposing effects on the catalytic activity of different S-helix variants. We conclude that the intervening HAMP domain passively transmits signals and shapes the signaling response depending on subtle changes in neighboring domains. This flexibility engenders a richness in functional outputs as HKs vary in response to changing evolutionary pressures.